1. 5.4 2.6 Section 2.5 Multiplication of Polynomials and Special Products1.
5.4
Exponents: Multiplying and Dividing Common Bases 1.
Multiplication of Polynomials 2.
Special Case Products: Difference of Squares and
Perfect Square Trinomials 1.
Introduction to Polynomials
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2. 5.4 2.6 Section 2.5 Multiplication of Polynomials and Special Products1.
5.4
Exponents: Multiplying and Dividing Common Bases
Any Homework Questions? 1.
Introduction to Polynomials
Slide 2
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3. 5.6 2.6 Multiplication of Polynomials and Special Products 1.
To multiply monomials, first use the associative and commutative properties of multiplication to group coefficients and like bases. Then simplify the result by using the properties of exponents.
Group coefficients and like bases.
Multiply the coefficients and add the exponents on x.
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Multiplying Monomials
Multiply.
Slide 4 1 a. b. c.
Multiplying Monomials
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Multiplying Monomials
Multiply.
Slide 5 1 a. b.
Multiplying Monomials
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6. 5.6 2 Multiplication of Polynomials and Special Products 1.
The distributive property is used to multiply polynomials:
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Multiplying a Polynomial by a Monomial
Multiply.
Slide 7 2
Multiplying a Polynomial by a Monomial a. b.
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8. Multiplying a Polynomial by a Monomial4
Multiplying a Polynomial by a Monomial a. b.
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9. 5.6 5 Multiplication of Polynomials and Special Products 1.
Next, the distributive property will be used to multiply polynomials with more than one term.
Note: Using the distributive property results in multiplying each term of the first polynomial by each term of the second polynomial.
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10. Multiplying a Polynomial by a Polynomial5
Multiplying a Polynomial by a Polynomial
Multiply the polynomials
Multiply each term in the first polynomial by each term in the second. That is, apply the distributive property.
Simplify.
Combine like terms.
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11. Notice that the product of two binomials equals the sum of the products of the First terms, the Outer terms, the Inner terms, and the Last terms.
The acronym FOIL (First Outer Inner Last) can be used as a memory device to multiply two binomials.
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Multiplying a Polynomial by a Polynomial
Multiply the polynomials.
Slide 12 4
Multiplying a Polynomial by a Polynomial
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Multiplying a Polynomial by a Polynomial
Multiply the polynomials.
Slide 13 4
Multiplying a Polynomial by a Polynomial
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14. Multiplying a Polynomial by a Polynomial8
Multiplying a Polynomial by a Polynomial
Multiply the polynomials.
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15. It is important to note that the acronym FOIL does not apply to Examples 9 and 10 because the product does not involve two binomials.
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Multiplying a Polynomial by a Polynomial
Multiply the polynomials.
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Multiplying a Polynomial by a Polynomial
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17. Multiplication of polynomials can be performed vertically by a process similar to column multiplication of real numbers. For example,
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Note: When multiplying by the column method, it is important to align like terms vertically before adding terms.
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Multiplying a Polynomial by a Polynomial
Multiply the polynomials.
Slide 18 5
Multiplying a Polynomial by a Polynomial
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19. 5.6 2.6 Multiplication of Polynomials and Special Products 2.
Special Case Products: Difference of Squares and
Perfect Square Trinomials
Multiplication of Polynomials and Special Products
In some cases the product of two binomials takes on a special pattern.
I. The first special case occurs when multiplying the sum and difference of the same two terms.

20. 5.6 2.6 Multiplication of Polynomials and Special Products 2.
Special Case Products: Difference of Squares and
Perfect Square Trinomials
Multiplication of Polynomials and Special Products
Notice that the middle terms are opposites. This leaves only the difference between the square of the first term and the square of the second term. For this reason, the product is called a difference of squares.

21. 5.6 2.6 Multiplication of Polynomials and Special Products 2.
Special Case Products: Difference of Squares and
Perfect Square Trinomials
Multiplication of Polynomials and Special Products
II. The second special case involves the square of a binomial.
The McGraw-

22. 5.6 2.6 Multiplication of Polynomials and Special Products 2.
Special Case Products: Difference of Squares and
Perfect Square Trinomials
Multiplication of Polynomials and Special Products
When squaring a binomial, the product will be a trinomial called a perfect square trinomial. The first and third terms are formed by squaring each term of the binomial. The middle term equals twice the product of the
terms in the binomial.
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23. 5.6 2.6 Multiplication of Polynomials and Special Products 2.
Special Case Products: Difference of Squares and
Perfect Square Trinomials
Multiplication of Polynomials and Special Products
Note: The expression
also expands to a perfect
square trinomial, but the middle term will be negative:
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24. FORMULA Special Case Product Formulas1.
The product is called a difference of squares.
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The product is called a perfect square
trinomial.
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Finding Special Products
Multiply.
Slide 25 6 a. b.
Finding Special Products
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26. The product can be checked by applying the distributive property or using FOIL .
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Squaring Binomials
Square the binomials.
Slide 27 7 a. b.
Finding Special Products
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28. The square of a binomial can be checked by explicitly writing the product of the two binomials and applying the distributive property or using FOIL.
Slide 28
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29. 5.4 2.6 Multiplication of Polynomials and Special Products 1.
Exponents: Multiplying and Dividing Common Bases 1.
Multiplication of Polynomials 2.
Special Case Products: Difference of Squares and
Perfect Square Trinomials 1.
Introduction to Polynomials
Slide 2929
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30. You Try:
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31. You Try:
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32. You Try:
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